Cluster extraction and annotation strategies on tabular datasets with diverse feature types¶

Importing necessary libraries¶

In [1]:
import numpy as np
import pandas as pd
from sklearn.preprocessing import StandardScaler
import matplotlib.pyplot as plt
import seaborn as sns
%matplotlib inline
import warnings
warnings.filterwarnings('ignore')
import tensorflow as tf
from tensorflow import keras
import umap.umap_ as umap
%config InlineBackend.figure_format = 'svg'

Importing pre-processed data¶

In [2]:
np.random.seed(42)
pd.set_option('display.max_columns', None)
pd.set_option('display.max_rows', 100)
data=pd.read_csv('Preprocessed_DM_xx.csv')
In [3]:
np.random.seed(42)
data=data.sample(frac=1) #Shuffle the data set

Feature engineering¶

  • Creating new feature called hypertension
  • Filtering unnecessary details
In [4]:
np.random.seed(42)
HTN_indexes=data.loc[(data['Currently.taking.a.prescribed.medicine.to.lower.BP'] != 0) | (data['First.SYSTOLIC.reading'] >= 140) | (data['First.DIASTOLIC.reading'] >= 90) ].index.values
HTN_cols=np.zeros(data.shape[0])
HTN_cols[[HTN_indexes]]=1
data['HTN']=HTN_cols
data=data.drop(["First.SYSTOLIC.reading","First.DIASTOLIC.reading","Currently.taking.a.prescribed.medicine.to.lower.BP"], axis=1)
data=data.reset_index(drop=True)
data.columns
data=data.drop(["Hb_adjust_alt_smok","Second.SYSTOLIC.reading","Second.DIASTOLIC.reading","Third.SYSTOLIC.reading","Third.DIASTOLIC.reading","Hb_status","Glucose.level",'SBP_status'], axis=1)
data=data.loc[data['BMI'] != 99.99]
data=data.loc[data['Hemoglobin.level..g.dl...1.decimal.'] != 99.99]
data=data.loc[data['Currently.has.asthma'] != .5]
data=data.loc[data['Currently.has.thyroid.disorder'] != .5]
data=data.loc[data['Currently.has.heart.disease'] != .5]
data=data.loc[data['Currently.has.cancer'] != .5]
data=data.loc[data['DM_history'] == 1]
data=data.loc[data['Type.of.caste.or.tribe.of.the.household.head'] != 0]
data=data.loc[data['Time.to.get.to.water.source..minutes.'] != -1]
data=data.drop(["Unnamed: 0","DM_status","DM_history"], axis=1)
In [5]:
np.random.seed(42)
i=[x for x in range(10125)]

data.set_index(pd.Series(i), inplace=True) # Reset the index

Spliting features¶

Creating 2 new dataframes: "data_disease" with features related to disease and "data_others" with rest of the features

In [6]:
data_disease= data[['Currently.has.asthma',
       'Currently.has.thyroid.disorder', 'Currently.has.heart.disease',
       'Currently.has.cancer', 'Suffers.from.TB','HTN']]
In [7]:
data_others= data[['Drinks.alcohol', 'Smoking_stat','Has.refrigerator',
       'Has.bicycle', 'Has.motorcycle.scooter', 'Has.car.truck', 'Owns.livestock..herds.or.farm.animals','Frequency.takes.milk.or.curd',
       'Frequency.eats.pulses.or.beans',
       'Frequency.eats.dark.green.leafy.vegetable', 'Frequency.eats.fruits',
       'Frequency.eats.eggs', 'Frequency.eats.fish',
       'Frequency.eats.chicken.or.meat', 'Frequency.eats.fried.food',
       'Frequency.takes.aerated.drinks','Frequency.household.members.smoke.inside.the.house','Wealth.index',
       'Highest.educational.level', 'Current.age','BMI','Hemoglobin.level..g.dl...1.decimal.','Time.to.get.to.water.source..minutes.', 'Household.head.s.religion', 'Sex', 'Type.of.place.of.residence', 'Household.structure',
       'Type.of.caste.or.tribe.of.the.household.head','Type.of.cooking.fuel','Source.of.drinking.water']]

Function for dimension reduction using UMAP¶

In [8]:
def feature_clustering(UMAP_neb,min_dist_UMAP, metric, data, visual):
    import umap.umap_ as umap
    np.random.seed(42)
    data_embedded = umap.UMAP(n_neighbors=UMAP_neb, min_dist=min_dist_UMAP, n_components=2, metric=metric, random_state=42).fit_transform(data)
    data_embedded[:,0]=(data_embedded[:,0]- np.mean(data_embedded[:,0]))/np.std(data_embedded[:,0])
    data_embedded[:,1]=(data_embedded[:,1]- np.mean(data_embedded[:,1]))/np.std(data_embedded[:,1])
    result = pd.DataFrame(data = data_embedded , 
        columns = ['UMAP_0', 'UMAP_1'])
    if visual==1:
        sns.lmplot( x="UMAP_0", y="UMAP_1",data=result,fit_reg=False,legend=False,scatter_kws={"s": 3},palette=customPalette_set1) # specify the point size
        #plt.savefig('clusters_umap_all.png', dpi=700, bbox_inches='tight')
        plt.show()
    else:
        pass
    return result

Dividing features¶

  • ord_list=ordinal features
  • cont_list=continueous features
  • nom_list=nominal features
In [9]:
ord_list=['Drinks.alcohol', 'Smoking_stat','Has.refrigerator',
       'Has.bicycle', 'Has.motorcycle.scooter', 'Has.car.truck', 'Owns.livestock..herds.or.farm.animals','Frequency.takes.milk.or.curd',
       'Frequency.eats.pulses.or.beans',
       'Frequency.eats.dark.green.leafy.vegetable', 'Frequency.eats.fruits',
       'Frequency.eats.eggs', 'Frequency.eats.fish',
       'Frequency.eats.chicken.or.meat', 'Frequency.eats.fried.food',
       'Frequency.takes.aerated.drinks','Frequency.household.members.smoke.inside.the.house','Wealth.index',
       'Highest.educational.level' ]
cont_list=['Current.age','BMI','Hemoglobin.level..g.dl...1.decimal.','Time.to.get.to.water.source..minutes.']
nom_list=['Household.head.s.religion', 'Sex', 'Type.of.place.of.residence', 'Household.structure',
       'Type.of.caste.or.tribe.of.the.household.head','Type.of.cooking.fuel','Source.of.drinking.water']

Function for Feature-type Distributed Clustering(FDC)¶

Function parameters:¶

  • data=dataframe on which feature distributed clustering should be performed
  • cont_list=list of continueous features
  • nom_list=list of nominal features
  • ord_list=list of ordinal features
  • cont_metric=distance metric for continueous data
  • ord_metric=distance metric for ordinal data
  • nom_metric=distance metric for nominal data
  • drop_nominal=1(to drop nominal data) or 0(don't drop nominal data)
  • visual=1(to plot the data) or 0(don't plot the data)
In [10]:
def FDC(data,cont_list,nom_list,ord_list,cont_metric, ord_metric, nom_metric, drop_nominal, visual):
    np.random.seed(42)
    colors_set1 = ["lightcoral", "lightseagreen", "mediumorchid", "orange", "burlywood", "cornflowerblue", "plum", "yellowgreen"]
    customPalette_set1 = sns.set_palette(sns.color_palette(colors_set1))
    cont_df=data[cont_list]
    nom_df=data[nom_list]
    ord_df=data[ord_list]
    cont_emb=feature_clustering(30,0.1, cont_metric, cont_df, 0) #Reducing continueous features into 2dim
    ord_emb=feature_clustering(30,0.1, ord_metric, ord_df, 0) #Reducing ordinal features into 2dim
    nom_emb=feature_clustering(30,0.1, nom_metric, nom_df, 0) #Reducing nominal features into 2dim
    if drop_nominal==1:
        result_concat=pd.concat([ord_emb, cont_emb, nom_emb.drop(['UMAP_1'],axis=1)],axis=1) #concatinating all reduced dimensions to get 5D embedding(1D from nominal)
    else:
        result_concat=pd.concat([ord_emb, cont_emb, nom_emb],axis=1)
    data_embedded = umap.UMAP(n_neighbors=30, min_dist=0.001, n_components=2, metric='euclidean', random_state=42).fit_transform(result_concat) #reducing 5D embedding to 2D using UMAP
    result_reduced = pd.DataFrame(data = data_embedded , 
        columns = ['UMAP_0', 'UMAP_1'])
    
    if visual==1:
        sns.lmplot( x="UMAP_0", y="UMAP_1",data=result_reduced,fit_reg=False,legend=False,scatter_kws={"s": 3},palette=customPalette_set1) # specify the point size
        plt.show()
        #plt.savefig('clusters_umap_all.png', dpi=700, bbox_inches='tight')
    else:
        pass
    return result_concat, result_reduced #returns both 5D and 2D embedding
In [11]:
# applying Feature Distributed Clustering(FDC) on entire 10125 data with all features except disease features
entire_data_FDC_emb_five,entire_data_FDC_emb_two=FDC(data_others,cont_list,nom_list,ord_list,'euclidean','canberra','hamming',1,1)
2022-08-17T13:58:42.112848 image/svg+xml Matplotlib v3.5.1, https://matplotlib.org/

DBSCAN clustering on FDC embedding¶

In [12]:
def db_scan(eps,min_samples,five_d_embedding,two_d_embedding,visual, pal):
    from sklearn.cluster import DBSCAN
    dbscan = DBSCAN(eps=eps, min_samples = min_samples)
    clusters=dbscan.fit_predict(five_d_embedding)
    (values,counts) = np.unique(clusters,return_counts=True)
    two_d_embedding['Cluster'] = clusters
    
    if visual==1:
        sns.lmplot( x="UMAP_0", y="UMAP_1",
        data=two_d_embedding,
        fit_reg=False, 
        legend=True,
        hue='Cluster', # color by cluster
        scatter_kws={"s": 3},palette=pal) # specify the point size
        plt.savefig('dbscan_ref_5dim.png', dpi=700, bbox_inches='tight')
        plt.show()
    else:
        pass
    return two_d_embedding.Cluster.to_list(),counts
In [13]:
#setting color palette for visualization of clusters
colors_set1 = ['lightgray','lightcoral','cornflowerblue','orange','mediumorchid', 'lightseagreen','olive', 'chocolate','steelblue']
customPalette_set1 = sns.set_palette(sns.color_palette(colors_set1))


#Applying clustering algorithm on FDC embedding from entire data
entire_data_cluster_list,entire_data_cluster_counts=db_scan(0.8,160,entire_data_FDC_emb_five,entire_data_FDC_emb_two,1,customPalette_set1)
2022-08-17T13:58:44.146094 image/svg+xml Matplotlib v3.5.1, https://matplotlib.org/
In [14]:
#Getting noise indices
non_noise_indices= np.where(np.array(entire_data_cluster_list)!=-1)

#Removing noise/outlires from FDC embedding and from entire data
entire_data_FDC_emb_five= entire_data_FDC_emb_five.iloc[non_noise_indices]
entire_data_FDC_emb_two= entire_data_FDC_emb_two.iloc[non_noise_indices]
entire_data_cluster_list= np.array(entire_data_cluster_list)[non_noise_indices]
data_others= data_others.iloc[non_noise_indices]

#Creating new cloumn for storing cluster labels 
data_others['cluster_labels']= entire_data_cluster_list

#getting binary representation for cluster labels
data_others= pd.get_dummies(data=data_others, columns=['cluster_labels'])
In [15]:
#Getting column names of encoded cluster labels
cluster_column_names=data_others.columns[-len(np.unique(entire_data_cluster_list)):].to_list()

Dividing data set for experiments¶

In [16]:
#75%  of entire data for training
np.random.seed(42)
data=data_others.sample(frac=0.75) # Training data
In [17]:
#Another 25% of entire data for validation
np.random.seed(42)
data_val=data_others.drop(data.index) # Validation data

Dividing training data into 3 folds¶

In [18]:
#Dividing training data into three folds

np.random.seed(42)
df_1=data.sample(frac=0.33) #fold 1

df=data.drop(df_1.index)
df_2=df.sample(frac=0.51) #fold 2

df_3=df.drop(df_2.index) #fold 3
In [19]:
np.random.seed(42)
#Possible combinations of concating 2 folds for training and using remaining fold for testing
training_folds=[pd.concat([df_1,df_2],axis=0), pd.concat([df_2,df_3],axis=0), pd.concat([df_3,df_1],axis=0)]
testing_folds=[df_3,df_1,df_2]

Function for neural network¶

Function parameters:¶

  • n_features= dimension of input data
  • hidden_dim1= dimension of first hidden layer
  • hidden_dim2= dimension of second hidden layer
  • out_emb_size= dimension of output data
  • act1= first hidden layer activation function
  • act2= second hidden layer activation function
In [20]:
def neural_network(n_features,hidden_dim1,hidden_dim2,out_emb_size,act1,act2,loss):
    np.random.seed(42)
    tf.random.set_seed(42)
    model=keras.Sequential([
         keras.layers.Dense(hidden_dim1,input_dim=n_features,activation=act1),
         keras.layers.Dense(hidden_dim1,activation=act2),
         keras.layers.Dense(out_emb_size)])
    model.compile(optimizer="adam" ,
              loss=loss, 
              metrics=['mse'])
    return model

Function for Cluster Incidence Matrix(CIM)¶

  • creating a matrix to evaluate the performance based on predicted cluster labels
In [21]:
def cluster_incidence_matrix_mod(cluster_list_new):
    np.random.seed(42)
    
    matrix=np.zeros((len(cluster_list_new),len(cluster_list_new)))
    for i in range(len(cluster_list_new)):
        for j in range(len(cluster_list_new)):
                if cluster_list_new[i]==cluster_list_new[j]:
                    matrix[i,j]=1 
                else:
                    pass
    
    return matrix
In [22]:
#Function for decoding the encoded cluster labels
def label_decoder(label_dataframe):
    label_array=np.array(label_dataframe)
    decoded_labels=[]
    for i in label_array:
        max_val=np.argmax(i)
        decoded_labels.append(max_val)
    return decoded_labels
In [23]:
colnames=[]
for i in range(len(entire_data_FDC_emb_five.columns)):
    colnames.append('c'+str(i+1))
In [24]:
np.random.seed(42)
count=0
fold_readings=[]
while count<3:
    FDC_emb_five_train=entire_data_FDC_emb_five.loc[list(training_folds[count].index)] #5D FDC embedding of training folds from entire training data
    FDC_emb_two_train=entire_data_FDC_emb_two.loc[list(training_folds[count].index)] #2D embeddings of training folds from entire training data
    FDC_emb_five_train.columns=colnames
    
    #Thirty dimensional data of training fold as features_matrix(X_train) 
    features_matrix=np.array(training_folds[count].drop(cluster_column_names, axis=1,inplace=False)) #X_train
    
    #Five dimensional FDC embeddings of training fold as target_matrix(y_train)
    target_matrix=np.array(FDC_emb_five_train) #y_train
    
    #Train a neural network to get five dimensional embedding
    model_1=neural_network(len(features_matrix[0]),int(0.6*len(features_matrix[0])),int(0.36*len(features_matrix[0])),len(target_matrix[0]),"relu","sigmoid","mse")
    history=model_1.fit(features_matrix,target_matrix,epochs=30,batch_size=8)
    print('\n')
    print('Training history across epochs for fold ',count+1)
    plt.plot(history.history['mse'],'r')
    plt.ylabel('mse')
    plt.xlabel('epoch')
    plt.show()
    
    #Using same thirty dimensional features_matrix(X_train) from first neural network and encoded cluster labels of training fold as target_labels_matrix(y_train) 
    target_labels_matrix=np.array(training_folds[count].loc[:,cluster_column_names]) #y
    
    
    #Train a neural network to get encoded cluster labels
    model_2=neural_network(len(features_matrix[0]),int(0.6*len(features_matrix[0])),int(0.36*len(features_matrix[0])),len(target_labels_matrix[0]),"relu","softmax","mse")
    history=model_2.fit(features_matrix,target_labels_matrix,epochs=30,batch_size=8)
    print('\n')
    print('Training history across epochs for fold ',count+1)
    plt.plot(history.history['mse'],'r')
    plt.ylabel('mse')
    plt.xlabel('epoch')
    plt.show()
    
    #Decoding cluster labels of training fold
    decoded_target_labels_matrix=label_decoder(target_labels_matrix)

    #Actual encoded cluster labels of testing fold for metric calculation  
    ref_clusters=testing_folds[count].loc[:,cluster_column_names] 
    #Decoding encoded cluster labels of testing fold
    decoded_ref_clusters=label_decoder(ref_clusters)
    

    #predicting testing fold to get five dim embedding using trained model_1
    testing_data=testing_folds[count].drop(cluster_column_names, axis=1,inplace=False)
    predicted_5dim=pd.DataFrame(model_1.predict(testing_data), columns=colnames)
    
    #UMAP on predicted 5D embedding
    predicted_2dim=feature_clustering(30,0.01, "euclidean", predicted_5dim, 0)

    #predicting testing fold to get encoded cluster labels using trained model_2
    predicted_clusters=pd.DataFrame(model_2.predict(testing_data))
    
    #Decoding predicted encoded cluster labels
    decoded_predicted_clusters=label_decoder(predicted_clusters)
    
    
    #concatinating training and predicted 5D embedding
    concatenated_5dim=pd.concat([FDC_emb_five_train,predicted_5dim])
    
    #UMAP on concatinated embedding
    two_dim_viz=feature_clustering(30, 0.01, 'euclidean', concatenated_5dim, 0)
    
    #Concatinating decoded cluster labels of training fold and predicted testing fold
    concatenated_cluster_labels=np.concatenate([np.array(decoded_target_labels_matrix),np.array(decoded_predicted_clusters)+len(np.unique(decoded_target_labels_matrix))])
    
    two_dim_viz['Cluster']= concatenated_cluster_labels
    
    
    #Setting dark colors for training folds    
    darkerhues=['lightcoral','cornflowerblue','orange','mediumorchid', 'lightseagreen','olive', 'chocolate','steelblue']
    colors_set2=[]
    for i in range(len(np.unique(decoded_target_labels_matrix))):
        colors_set2.append(darkerhues[i])
    
    #Concatinating dark colors for training folds and corresponding light colors for testing folds
    colors_set2=colors_set2+["lightpink", 'skyblue', 'wheat', "plum","paleturquoise",  "lightgreen",  'burlywood','lightsteelblue']
    
    print('Vizualization for FDC for training fold (shown in dark hue) '+str(count+1) + 'and predicted clusters from neural network on testing fold (shown in corresponding light hues) '+str(count+1))
    
    #visualizing the clusters of both training and testing folds
    sns.lmplot( x="UMAP_0", y="UMAP_1", data=two_dim_viz, fit_reg=False, legend=False, hue='Cluster', scatter_kws={"s": 3},palette=sns.set_palette(sns.color_palette(colors_set2))) 
    plt.show()
    
    #Metric calculation

    CIM_predicted=cluster_incidence_matrix_mod(np.array(decoded_predicted_clusters))#Cluster incidence metric for predicted clusters
    CIM_reference=cluster_incidence_matrix_mod(np.array(decoded_ref_clusters))#Cluster incidence metric for reference clusters
    Product=np.dot(CIM_predicted,CIM_reference)
    cluster_incdences_in_data=np.sum(CIM_reference,axis=1)  
    mean_points_in_same_clusters=np.mean(np.diagonal(Product)/cluster_incdences_in_data)
    fold_readings.append(mean_points_in_same_clusters*100)
    
    print("Average percentage of patients belongs to the same cluster is: {}%".format(mean_points_in_same_clusters*100))
    print('\n')
    count+=1


print('\n')
print('\n')

Epoch 1/30
428/428 [==============================] - 1s 960us/step - loss: 0.6358 - mse: 0.6358
Epoch 2/30
428/428 [==============================] - 0s 975us/step - loss: 0.3503 - mse: 0.3503
Epoch 3/30
428/428 [==============================] - 0s 978us/step - loss: 0.2446 - mse: 0.2446
Epoch 4/30
428/428 [==============================] - 0s 951us/step - loss: 0.1981 - mse: 0.1981
Epoch 5/30
428/428 [==============================] - 0s 972us/step - loss: 0.1758 - mse: 0.1758
Epoch 6/30
428/428 [==============================] - 0s 964us/step - loss: 0.1607 - mse: 0.1607
Epoch 7/30
428/428 [==============================] - 0s 962us/step - loss: 0.1494 - mse: 0.1494
Epoch 8/30
428/428 [==============================] - 0s 951us/step - loss: 0.1404 - mse: 0.1404
Epoch 9/30
428/428 [==============================] - 0s 959us/step - loss: 0.1344 - mse: 0.1344
Epoch 10/30
428/428 [==============================] - 0s 945us/step - loss: 0.1290 - mse: 0.1290
Epoch 11/30
428/428 [==============================] - 0s 952us/step - loss: 0.1232 - mse: 0.1232
Epoch 12/30
428/428 [==============================] - 0s 970us/step - loss: 0.1203 - mse: 0.1203
Epoch 13/30
428/428 [==============================] - 0s 947us/step - loss: 0.1166 - mse: 0.1166
Epoch 14/30
428/428 [==============================] - 0s 936us/step - loss: 0.1133 - mse: 0.1133
Epoch 15/30
428/428 [==============================] - 0s 948us/step - loss: 0.1097 - mse: 0.1097
Epoch 16/30
428/428 [==============================] - 0s 933us/step - loss: 0.1070 - mse: 0.1070
Epoch 17/30
428/428 [==============================] - 0s 926us/step - loss: 0.1044 - mse: 0.1044
Epoch 18/30
428/428 [==============================] - 0s 915us/step - loss: 0.1027 - mse: 0.1027
Epoch 19/30
428/428 [==============================] - 0s 945us/step - loss: 0.1004 - mse: 0.1004
Epoch 20/30
428/428 [==============================] - 0s 976us/step - loss: 0.0988 - mse: 0.0988
Epoch 21/30
428/428 [==============================] - 0s 978us/step - loss: 0.0960 - mse: 0.0960
Epoch 22/30
428/428 [==============================] - 0s 955us/step - loss: 0.0945 - mse: 0.0945
Epoch 23/30
428/428 [==============================] - 0s 957us/step - loss: 0.0931 - mse: 0.0931
Epoch 24/30
428/428 [==============================] - 0s 951us/step - loss: 0.0910 - mse: 0.0910
Epoch 25/30
428/428 [==============================] - 0s 969us/step - loss: 0.0897 - mse: 0.0897
Epoch 26/30
428/428 [==============================] - 0s 962us/step - loss: 0.0886 - mse: 0.0886
Epoch 27/30
428/428 [==============================] - 0s 980us/step - loss: 0.0871 - mse: 0.0871
Epoch 28/30
428/428 [==============================] - 0s 981us/step - loss: 0.0862 - mse: 0.0862
Epoch 29/30
428/428 [==============================] - 0s 969us/step - loss: 0.0849 - mse: 0.0849
Epoch 30/30
428/428 [==============================] - 0s 959us/step - loss: 0.0841 - mse: 0.0841


Training history across epochs for fold  1
2022-08-17T13:58:58.497997 image/svg+xml Matplotlib v3.5.1, https://matplotlib.org/ 
Epoch 1/30
428/428 [==============================] - 1s 964us/step - loss: 0.1554 - mse: 0.1554
Epoch 2/30
428/428 [==============================] - 0s 964us/step - loss: 0.0948 - mse: 0.0948
Epoch 3/30
428/428 [==============================] - 0s 953us/step - loss: 0.0483 - mse: 0.0483
Epoch 4/30
428/428 [==============================] - 0s 991us/step - loss: 0.0295 - mse: 0.0295
Epoch 5/30
428/428 [==============================] - 0s 951us/step - loss: 0.0223 - mse: 0.0223
Epoch 6/30
428/428 [==============================] - 0s 959us/step - loss: 0.0184 - mse: 0.0184
Epoch 7/30
428/428 [==============================] - 0s 968us/step - loss: 0.0168 - mse: 0.0168
Epoch 8/30
428/428 [==============================] - 0s 951us/step - loss: 0.0158 - mse: 0.0158
Epoch 9/30
428/428 [==============================] - 0s 963us/step - loss: 0.0142 - mse: 0.0142
Epoch 10/30
428/428 [==============================] - 0s 986us/step - loss: 0.0139 - mse: 0.0139
Epoch 11/30
428/428 [==============================] - 0s 953us/step - loss: 0.0136 - mse: 0.0136
Epoch 12/30
428/428 [==============================] - 0s 951us/step - loss: 0.0126 - mse: 0.0126
Epoch 13/30
428/428 [==============================] - 0s 961us/step - loss: 0.0120 - mse: 0.0120
Epoch 14/30
428/428 [==============================] - 0s 944us/step - loss: 0.0113 - mse: 0.0113
Epoch 15/30
428/428 [==============================] - 0s 972us/step - loss: 0.0114 - mse: 0.0114
Epoch 16/30
428/428 [==============================] - 0s 962us/step - loss: 0.0110 - mse: 0.0110
Epoch 17/30
428/428 [==============================] - 0s 967us/step - loss: 0.0109 - mse: 0.0109
Epoch 18/30
428/428 [==============================] - 0s 955us/step - loss: 0.0105 - mse: 0.0105
Epoch 19/30
428/428 [==============================] - 0s 951us/step - loss: 0.0107 - mse: 0.0107
Epoch 20/30
428/428 [==============================] - 0s 966us/step - loss: 0.0107 - mse: 0.0107
Epoch 21/30
428/428 [==============================] - 0s 962us/step - loss: 0.0100 - mse: 0.0100
Epoch 22/30
428/428 [==============================] - 0s 953us/step - loss: 0.0100 - mse: 0.0100
Epoch 23/30
428/428 [==============================] - 0s 988us/step - loss: 0.0100 - mse: 0.0100
Epoch 24/30
428/428 [==============================] - 0s 967us/step - loss: 0.0094 - mse: 0.0094
Epoch 25/30
428/428 [==============================] - 0s 952us/step - loss: 0.0094 - mse: 0.0094
Epoch 26/30
428/428 [==============================] - 0s 985us/step - loss: 0.0094 - mse: 0.0094
Epoch 27/30
428/428 [==============================] - 0s 952us/step - loss: 0.0092 - mse: 0.0092
Epoch 28/30
428/428 [==============================] - 0s 967us/step - loss: 0.0093 - mse: 0.0093
Epoch 29/30
428/428 [==============================] - 0s 981us/step - loss: 0.0088 - mse: 0.0088
Epoch 30/30
428/428 [==============================] - 0s 970us/step - loss: 0.0089 - mse: 0.0089


Training history across epochs for fold  1
2022-08-17T13:59:11.327603 image/svg+xml Matplotlib v3.5.1, https://matplotlib.org/ 
53/53 [==============================] - 0s 601us/step
53/53 [==============================] - 0s 600us/step
Vizualization for FDC for training fold (shown in dark hue) 1and predicted clusters from neural network on testing fold (shown in corresponding light hues) 1
2022-08-17T13:59:28.012007 image/svg+xml Matplotlib v3.5.1, https://matplotlib.org/ 
Average percentage of patients belongs to the same cluster is: 92.93523126437462%


Epoch 1/30
427/427 [==============================] - 1s 948us/step - loss: 0.6127 - mse: 0.6127
Epoch 2/30
427/427 [==============================] - 0s 972us/step - loss: 0.3366 - mse: 0.3366
Epoch 3/30
427/427 [==============================] - 0s 959us/step - loss: 0.2426 - mse: 0.2426
Epoch 4/30
427/427 [==============================] - 0s 962us/step - loss: 0.1976 - mse: 0.1976
Epoch 5/30
427/427 [==============================] - 0s 990us/step - loss: 0.1772 - mse: 0.1772
Epoch 6/30
427/427 [==============================] - 0s 945us/step - loss: 0.1630 - mse: 0.1630
Epoch 7/30
427/427 [==============================] - 0s 974us/step - loss: 0.1513 - mse: 0.1513
Epoch 8/30
427/427 [==============================] - 0s 991us/step - loss: 0.1433 - mse: 0.1433
Epoch 9/30
427/427 [==============================] - 0s 952us/step - loss: 0.1373 - mse: 0.1373
Epoch 10/30
427/427 [==============================] - 0s 949us/step - loss: 0.1319 - mse: 0.1319
Epoch 11/30
427/427 [==============================] - 0s 953us/step - loss: 0.1270 - mse: 0.1270
Epoch 12/30
427/427 [==============================] - 0s 962us/step - loss: 0.1230 - mse: 0.1230
Epoch 13/30
427/427 [==============================] - 0s 964us/step - loss: 0.1188 - mse: 0.1188
Epoch 14/30
427/427 [==============================] - 0s 975us/step - loss: 0.1162 - mse: 0.1162
Epoch 15/30
427/427 [==============================] - 0s 970us/step - loss: 0.1137 - mse: 0.1137
Epoch 16/30
427/427 [==============================] - 0s 972us/step - loss: 0.1094 - mse: 0.1094
Epoch 17/30
427/427 [==============================] - 0s 991us/step - loss: 0.1077 - mse: 0.1077
Epoch 18/30
427/427 [==============================] - 0s 967us/step - loss: 0.1066 - mse: 0.1066
Epoch 19/30
427/427 [==============================] - 0s 936us/step - loss: 0.1035 - mse: 0.1035
Epoch 20/30
427/427 [==============================] - 0s 970us/step - loss: 0.1014 - mse: 0.1014
Epoch 21/30
427/427 [==============================] - 0s 953us/step - loss: 0.0990 - mse: 0.0990
Epoch 22/30
427/427 [==============================] - 0s 969us/step - loss: 0.0984 - mse: 0.0984
Epoch 23/30
427/427 [==============================] - 0s 973us/step - loss: 0.0971 - mse: 0.0971
Epoch 24/30
427/427 [==============================] - 0s 953us/step - loss: 0.0943 - mse: 0.0943
Epoch 25/30
427/427 [==============================] - 0s 969us/step - loss: 0.0931 - mse: 0.0931
Epoch 26/30
427/427 [==============================] - 0s 966us/step - loss: 0.0921 - mse: 0.0921
Epoch 27/30
427/427 [==============================] - 0s 974us/step - loss: 0.0902 - mse: 0.0902
Epoch 28/30
427/427 [==============================] - 0s 977us/step - loss: 0.0903 - mse: 0.0903
Epoch 29/30
427/427 [==============================] - 0s 953us/step - loss: 0.0879 - mse: 0.0879
Epoch 30/30
427/427 [==============================] - 0s 954us/step - loss: 0.0881 - mse: 0.0881


Training history across epochs for fold  2
2022-08-17T13:59:42.397537 image/svg+xml Matplotlib v3.5.1, https://matplotlib.org/ 
Epoch 1/30
427/427 [==============================] - 1s 967us/step - loss: 0.1532 - mse: 0.1532
Epoch 2/30
427/427 [==============================] - 0s 977us/step - loss: 0.0981 - mse: 0.0981
Epoch 3/30
427/427 [==============================] - 0s 982us/step - loss: 0.0493 - mse: 0.0493
Epoch 4/30
427/427 [==============================] - 0s 945us/step - loss: 0.0310 - mse: 0.0310
Epoch 5/30
427/427 [==============================] - 0s 964us/step - loss: 0.0249 - mse: 0.0249
Epoch 6/30
427/427 [==============================] - 0s 972us/step - loss: 0.0213 - mse: 0.0213
Epoch 7/30
427/427 [==============================] - 0s 955us/step - loss: 0.0192 - mse: 0.0192
Epoch 8/30
427/427 [==============================] - 0s 980us/step - loss: 0.0175 - mse: 0.0175
Epoch 9/30
427/427 [==============================] - 0s 976us/step - loss: 0.0159 - mse: 0.0159
Epoch 10/30
427/427 [==============================] - 0s 953us/step - loss: 0.0149 - mse: 0.0149
Epoch 11/30
427/427 [==============================] - 0s 985us/step - loss: 0.0143 - mse: 0.0143
Epoch 12/30
427/427 [==============================] - 0s 956us/step - loss: 0.0139 - mse: 0.0139
Epoch 13/30
427/427 [==============================] - 0s 965us/step - loss: 0.0134 - mse: 0.0134
Epoch 14/30
427/427 [==============================] - 0s 999us/step - loss: 0.0133 - mse: 0.0133
Epoch 15/30
427/427 [==============================] - 0s 953us/step - loss: 0.0129 - mse: 0.0129
Epoch 16/30
427/427 [==============================] - 0s 990us/step - loss: 0.0124 - mse: 0.0124
Epoch 17/30
427/427 [==============================] - 0s 935us/step - loss: 0.0125 - mse: 0.0125
Epoch 18/30
427/427 [==============================] - 0s 956us/step - loss: 0.0115 - mse: 0.0115
Epoch 19/30
427/427 [==============================] - 0s 963us/step - loss: 0.0117 - mse: 0.0117
Epoch 20/30
427/427 [==============================] - 0s 963us/step - loss: 0.0118 - mse: 0.0118
Epoch 21/30
427/427 [==============================] - 0s 952us/step - loss: 0.0110 - mse: 0.0110
Epoch 22/30
427/427 [==============================] - 0s 953us/step - loss: 0.0111 - mse: 0.0111
Epoch 23/30
427/427 [==============================] - 0s 992us/step - loss: 0.0108 - mse: 0.0108
Epoch 24/30
427/427 [==============================] - 0s 930us/step - loss: 0.0108 - mse: 0.0108
Epoch 25/30
427/427 [==============================] - 0s 955us/step - loss: 0.0107 - mse: 0.0107
Epoch 26/30
427/427 [==============================] - 0s 934us/step - loss: 0.0104 - mse: 0.0104
Epoch 27/30
427/427 [==============================] - 0s 976us/step - loss: 0.0101 - mse: 0.0101
Epoch 28/30
427/427 [==============================] - 0s 935us/step - loss: 0.0102 - mse: 0.0102
Epoch 29/30
427/427 [==============================] - 0s 963us/step - loss: 0.0099 - mse: 0.0099
Epoch 30/30
427/427 [==============================] - 0s 961us/step - loss: 0.0100 - mse: 0.0100


Training history across epochs for fold  2
2022-08-17T13:59:55.482578 image/svg+xml Matplotlib v3.5.1, https://matplotlib.org/ 
53/53 [==============================] - 0s 601us/step
53/53 [==============================] - 0s 900us/step
Vizualization for FDC for training fold (shown in dark hue) 2and predicted clusters from neural network on testing fold (shown in corresponding light hues) 2
2022-08-17T14:00:10.181401 image/svg+xml Matplotlib v3.5.1, https://matplotlib.org/ 
Average percentage of patients belongs to the same cluster is: 94.48229488578839%


Epoch 1/30
420/420 [==============================] - 1s 1ms/step - loss: 0.6235 - mse: 0.6235
Epoch 2/30
420/420 [==============================] - 0s 972us/step - loss: 0.3481 - mse: 0.3481
Epoch 3/30
420/420 [==============================] - 0s 973us/step - loss: 0.2440 - mse: 0.2440
Epoch 4/30
420/420 [==============================] - 0s 971us/step - loss: 0.2022 - mse: 0.2022
Epoch 5/30
420/420 [==============================] - 0s 971us/step - loss: 0.1798 - mse: 0.1798
Epoch 6/30
420/420 [==============================] - 0s 982us/step - loss: 0.1640 - mse: 0.1640
Epoch 7/30
420/420 [==============================] - 0s 1ms/step - loss: 0.1523 - mse: 0.1523
Epoch 8/30
420/420 [==============================] - 0s 989us/step - loss: 0.1443 - mse: 0.1443
Epoch 9/30
420/420 [==============================] - 0s 1ms/step - loss: 0.1373 - mse: 0.1373
Epoch 10/30
420/420 [==============================] - 0s 979us/step - loss: 0.1317 - mse: 0.1317
Epoch 11/30
420/420 [==============================] - 0s 1ms/step - loss: 0.1272 - mse: 0.1272
Epoch 12/30
420/420 [==============================] - 0s 1ms/step - loss: 0.1237 - mse: 0.1237
Epoch 13/30
420/420 [==============================] - 0s 996us/step - loss: 0.1201 - mse: 0.1201
Epoch 14/30
420/420 [==============================] - 0s 1ms/step - loss: 0.1170 - mse: 0.1170
Epoch 15/30
420/420 [==============================] - 0s 1ms/step - loss: 0.1139 - mse: 0.1139
Epoch 16/30
420/420 [==============================] - 0s 967us/step - loss: 0.1104 - mse: 0.1104
Epoch 17/30
420/420 [==============================] - 0s 994us/step - loss: 0.1069 - mse: 0.1069
Epoch 18/30
420/420 [==============================] - 0s 1ms/step - loss: 0.1048 - mse: 0.1048
Epoch 19/30
420/420 [==============================] - 0s 1ms/step - loss: 0.1034 - mse: 0.1034
Epoch 20/30
420/420 [==============================] - 0s 969us/step - loss: 0.1010 - mse: 0.1010
Epoch 21/30
420/420 [==============================] - 0s 997us/step - loss: 0.0995 - mse: 0.0995
Epoch 22/30
420/420 [==============================] - 0s 1ms/step - loss: 0.0973 - mse: 0.0973
Epoch 23/30
420/420 [==============================] - 0s 1ms/step - loss: 0.0962 - mse: 0.0962
Epoch 24/30
420/420 [==============================] - 0s 1ms/step - loss: 0.0942 - mse: 0.0942
Epoch 25/30
420/420 [==============================] - 0s 1ms/step - loss: 0.0921 - mse: 0.0921
Epoch 26/30
420/420 [==============================] - 0s 988us/step - loss: 0.0916 - mse: 0.0916
Epoch 27/30
420/420 [==============================] - 0s 1ms/step - loss: 0.0895 - mse: 0.0895
Epoch 28/30
420/420 [==============================] - 0s 984us/step - loss: 0.0884 - mse: 0.0884
Epoch 29/30
420/420 [==============================] - 0s 979us/step - loss: 0.0869 - mse: 0.0869
Epoch 30/30
420/420 [==============================] - 0s 1ms/step - loss: 0.0862 - mse: 0.0862


Training history across epochs for fold  3
2022-08-17T14:00:24.885676 image/svg+xml Matplotlib v3.5.1, https://matplotlib.org/ 
Epoch 1/30
420/420 [==============================] - 1s 975us/step - loss: 0.1529 - mse: 0.1529
Epoch 2/30
420/420 [==============================] - 0s 968us/step - loss: 0.0967 - mse: 0.0967
Epoch 3/30
420/420 [==============================] - 0s 979us/step - loss: 0.0507 - mse: 0.0507
Epoch 4/30
420/420 [==============================] - 0s 1ms/step - loss: 0.0321 - mse: 0.0321
Epoch 5/30
420/420 [==============================] - 0s 982us/step - loss: 0.0253 - mse: 0.0253
Epoch 6/30
420/420 [==============================] - 0s 1ms/step - loss: 0.0213 - mse: 0.0213
Epoch 7/30
420/420 [==============================] - 0s 1ms/step - loss: 0.0188 - mse: 0.0188
Epoch 8/30
420/420 [==============================] - 0s 1ms/step - loss: 0.0175 - mse: 0.0175
Epoch 9/30
420/420 [==============================] - 0s 984us/step - loss: 0.0163 - mse: 0.0163
Epoch 10/30
420/420 [==============================] - 0s 1ms/step - loss: 0.0149 - mse: 0.0149
Epoch 11/30
420/420 [==============================] - 0s 1ms/step - loss: 0.0144 - mse: 0.0144
Epoch 12/30
420/420 [==============================] - 0s 1ms/step - loss: 0.0134 - mse: 0.0134
Epoch 13/30
420/420 [==============================] - 0s 993us/step - loss: 0.0136 - mse: 0.0136
Epoch 14/30
420/420 [==============================] - 0s 1ms/step - loss: 0.0134 - mse: 0.0134
Epoch 15/30
420/420 [==============================] - 0s 1ms/step - loss: 0.0125 - mse: 0.0125
Epoch 16/30
420/420 [==============================] - 0s 979us/step - loss: 0.0126 - mse: 0.0126
Epoch 17/30
420/420 [==============================] - 0s 1000us/step - loss: 0.0120 - mse: 0.0120
Epoch 18/30
420/420 [==============================] - 0s 976us/step - loss: 0.0114 - mse: 0.0114
Epoch 19/30
420/420 [==============================] - 0s 1ms/step - loss: 0.0116 - mse: 0.0116
Epoch 20/30
420/420 [==============================] - 0s 985us/step - loss: 0.0111 - mse: 0.0111
Epoch 21/30
420/420 [==============================] - 0s 973us/step - loss: 0.0105 - mse: 0.0105
Epoch 22/30
420/420 [==============================] - 0s 975us/step - loss: 0.0105 - mse: 0.0105
Epoch 23/30
420/420 [==============================] - 0s 1ms/step - loss: 0.0102 - mse: 0.0102
Epoch 24/30
420/420 [==============================] - 0s 990us/step - loss: 0.0102 - mse: 0.0102
Epoch 25/30
420/420 [==============================] - 0s 1ms/step - loss: 0.0097 - mse: 0.0097
Epoch 26/30
420/420 [==============================] - 0s 989us/step - loss: 0.0099 - mse: 0.0099
Epoch 27/30
420/420 [==============================] - 0s 1ms/step - loss: 0.0090 - mse: 0.0090
Epoch 28/30
420/420 [==============================] - 0s 1ms/step - loss: 0.0094 - mse: 0.0094
Epoch 29/30
420/420 [==============================] - 0s 983us/step - loss: 0.0088 - mse: 0.0088
Epoch 30/30
420/420 [==============================] - 0s 1ms/step - loss: 0.0087 - mse: 0.0087


Training history across epochs for fold  3
2022-08-17T14:00:38.039749 image/svg+xml Matplotlib v3.5.1, https://matplotlib.org/ 
55/55 [==============================] - 0s 579us/step
55/55 [==============================] - 0s 578us/step
Vizualization for FDC for training fold (shown in dark hue) 3and predicted clusters from neural network on testing fold (shown in corresponding light hues) 3
2022-08-17T14:00:53.243307 image/svg+xml Matplotlib v3.5.1, https://matplotlib.org/ 
Average percentage of patients belongs to the same cluster is: 94.86220026658046%
In [25]:
print('Average percentage of patients belonging to the same cluster over all three folds:', np.mean(np.array(fold_readings)))

Average percentage of patients belonging to the same cluster over all three folds: 94.09324213891449

Validation¶

In [26]:
np.random.seed(42)

FDC_emb_five_data=entire_data_FDC_emb_five.loc[list(data.index)] #5D FDC embedding of training fold from entire data
FDC_emb_two_data=entire_data_FDC_emb_two.loc[list(data.index)] #2D embedding of training fold from entire data
FDC_emb_five_data.columns=colnames

#Thirty dimensional data of training fold as features_matrix(X_train) 
features_matrix=np.array(data.drop(cluster_column_names, axis=1,inplace=False)) #X_train

#Five dimensional FDC embedding of training fold as target_matrix(y_train)
target_matrix=np.array(FDC_emb_five_data) #y_train

#Train a neural network to get five dimensional embedding
model_1=neural_network(len(features_matrix[0]),int(0.6*len(features_matrix[0])),int(0.36*len(features_matrix[0])),len(target_matrix[0]),"relu","sigmoid","mse")
history=model_1.fit(features_matrix,target_matrix,epochs=30,batch_size=8)
print('\n')
print('Training history across epochs for training data ')
plt.plot(history.history['mse'],'r')
plt.ylabel('mse')
plt.xlabel('epoch')
plt.show()

#Using same thirty dimensional features_matrix(X_train) from first neural network and encoded cluster labels of training fold as target_labels_matrix(y_train) 
target_labels_matrix=np.array(data.loc[:,cluster_column_names]) #y


#Train a neural network to get encoded cluster labels
model_2=neural_network(len(features_matrix[0]),int(0.6*len(features_matrix[0])),int(0.36*len(features_matrix[0])),len(target_labels_matrix[0]),"relu","softmax","mse")
history=model_2.fit(features_matrix,target_labels_matrix,epochs=30,batch_size=8)
print('\n')
print('Training history across epochs for training data ')
plt.plot(history.history['mse'],'r')
plt.ylabel('mse')
plt.xlabel('epoch')
plt.show()

#Decoding cluster labels of training fold
decoded_target_labels_matrix=label_decoder(target_labels_matrix)

#Actual encoded cluster labels of validation data for metric calculation  
ref_clusters=data_val.loc[:,cluster_column_names] 
#Decoding encoded cluster labels of validation data
decoded_ref_clusters=label_decoder(ref_clusters)


#predicting validation data to get five dim embedding using trained model_1
validation_data=data_val.drop(cluster_column_names, axis=1,inplace=False)
predicted_5dim=pd.DataFrame(model_1.predict(validation_data), columns=colnames)

#UMAP on predicted 5D embedding
predicted_2dim=feature_clustering(30,0.01, "euclidean", predicted_5dim, 0)

#predicting validation data to get encoded cluster labels using trained model_2
predicted_clusters=pd.DataFrame(model_2.predict(validation_data))

#Decoding predicted encoded cluster labels
decoded_predicted_clusters=label_decoder(predicted_clusters)


#concatinating training and predicted 5D embedding
concatenated_5dim=pd.concat([FDC_emb_five_data,predicted_5dim])

#UMAP on concatinated embedding
two_dim_viz=feature_clustering(30, 0.01, 'euclidean', concatenated_5dim, 0)

#Concatinating decoded cluster labels of training data and predicted validation data
concatenated_cluster_labels=np.concatenate([np.array(decoded_target_labels_matrix),np.array(decoded_predicted_clusters)+len(np.unique(decoded_target_labels_matrix))])

two_dim_viz['Cluster']= concatenated_cluster_labels



#Setting dark colors for training data    
darkerhues=['lightcoral','cornflowerblue','orange','mediumorchid', 'lightseagreen','olive', 'chocolate','steelblue']
colors_set2=[]
for i in range(len(np.unique(decoded_target_labels_matrix))):
    colors_set2.append(darkerhues[i])

#Concatinating dark colors for training data and corresponding light colors for validation data
colors_set2=colors_set2+["lightpink", 'skyblue', 'wheat', "plum","paleturquoise",  "lightgreen",  'burlywood','lightsteelblue']

print('Vizualization for FDC for training data (shown in dark hue) '+ 'and predicted clusters from neural network on validation data (shown in corresponding light hues) ')

#visualizing the clusters of both training and validation data
sns.lmplot( x="UMAP_0", y="UMAP_1", data=two_dim_viz, fit_reg=False, legend=False, hue='Cluster', scatter_kws={"s": 3},palette=sns.set_palette(sns.color_palette(colors_set2))) 
plt.show()

#Metric calculation

CIM_predicted=cluster_incidence_matrix_mod(np.array(decoded_predicted_clusters))#Cluster incidence metric for predicted clusters
CIM_reference=cluster_incidence_matrix_mod(np.array(decoded_ref_clusters))#Cluster incidence metric for reference clusters
Product=np.dot(CIM_predicted,CIM_reference)
cluster_incidences_in_data=np.sum(CIM_reference,axis=1)  
mean_points_in_same_clusters=np.mean(np.diagonal(Product)/cluster_incidences_in_data)
fold_readings.append(mean_points_in_same_clusters*100)

print("Average percentage of patients belongs to the same cluster is: {}%".format(mean_points_in_same_clusters*100))
print('\n')



print('\n')
print('\n')

Epoch 1/30
638/638 [==============================] - 1s 995us/step - loss: 0.5342 - mse: 0.5342
Epoch 2/30
638/638 [==============================] - 1s 974us/step - loss: 0.2610 - mse: 0.2610
Epoch 3/30
638/638 [==============================] - 1s 985us/step - loss: 0.1955 - mse: 0.1955
Epoch 4/30
638/638 [==============================] - 1s 994us/step - loss: 0.1684 - mse: 0.1684
Epoch 5/30
638/638 [==============================] - 1s 992us/step - loss: 0.1517 - mse: 0.1517
Epoch 6/30
638/638 [==============================] - 1s 991us/step - loss: 0.1403 - mse: 0.1403
Epoch 7/30
638/638 [==============================] - 1s 996us/step - loss: 0.1321 - mse: 0.1321
Epoch 8/30
638/638 [==============================] - 1s 1ms/step - loss: 0.1272 - mse: 0.1272
Epoch 9/30
638/638 [==============================] - 1s 1ms/step - loss: 0.1224 - mse: 0.1224
Epoch 10/30
638/638 [==============================] - 1s 996us/step - loss: 0.1189 - mse: 0.1189
Epoch 11/30
638/638 [==============================] - 1s 996us/step - loss: 0.1155 - mse: 0.1155
Epoch 12/30
638/638 [==============================] - 1s 984us/step - loss: 0.1113 - mse: 0.1113
Epoch 13/30
638/638 [==============================] - 1s 998us/step - loss: 0.1077 - mse: 0.1077
Epoch 14/30
638/638 [==============================] - 1s 1ms/step - loss: 0.1050 - mse: 0.1050
Epoch 15/30
638/638 [==============================] - 1s 1ms/step - loss: 0.1014 - mse: 0.1014
Epoch 16/30
638/638 [==============================] - 1s 991us/step - loss: 0.0994 - mse: 0.0994
Epoch 17/30
638/638 [==============================] - 1s 1ms/step - loss: 0.0962 - mse: 0.0962
Epoch 18/30
638/638 [==============================] - 1s 994us/step - loss: 0.0940 - mse: 0.0940
Epoch 19/30
638/638 [==============================] - 1s 989us/step - loss: 0.0929 - mse: 0.0929
Epoch 20/30
638/638 [==============================] - 1s 999us/step - loss: 0.0905 - mse: 0.0905
Epoch 21/30
638/638 [==============================] - 1s 983us/step - loss: 0.0886 - mse: 0.0886
Epoch 22/30
638/638 [==============================] - 1s 986us/step - loss: 0.0870 - mse: 0.0870
Epoch 23/30
638/638 [==============================] - 1s 984us/step - loss: 0.0860 - mse: 0.0860
Epoch 24/30
638/638 [==============================] - 1s 989us/step - loss: 0.0844 - mse: 0.0844
Epoch 25/30
638/638 [==============================] - 1s 995us/step - loss: 0.0837 - mse: 0.0837
Epoch 26/30
638/638 [==============================] - 1s 989us/step - loss: 0.0822 - mse: 0.0822
Epoch 27/30
638/638 [==============================] - 1s 1ms/step - loss: 0.0812 - mse: 0.0812
Epoch 28/30
638/638 [==============================] - 1s 976us/step - loss: 0.0795 - mse: 0.0795
Epoch 29/30
638/638 [==============================] - 1s 1ms/step - loss: 0.0792 - mse: 0.0792
Epoch 30/30
638/638 [==============================] - 1s 985us/step - loss: 0.0778 - mse: 0.0778


Training history across epochs for training data
2022-08-17T14:01:14.664343 image/svg+xml Matplotlib v3.5.1, https://matplotlib.org/ 
Epoch 1/30
638/638 [==============================] - 1s 974us/step - loss: 0.1380 - mse: 0.1380
Epoch 2/30
638/638 [==============================] - 1s 1ms/step - loss: 0.0632 - mse: 0.0632
Epoch 3/30
638/638 [==============================] - 1s 1ms/step - loss: 0.0296 - mse: 0.0296
Epoch 4/30
638/638 [==============================] - 1s 985us/step - loss: 0.0221 - mse: 0.0221
Epoch 5/30
638/638 [==============================] - 1s 1ms/step - loss: 0.0185 - mse: 0.0185
Epoch 6/30
638/638 [==============================] - 1s 1ms/step - loss: 0.0164 - mse: 0.0164
Epoch 7/30
638/638 [==============================] - 1s 1ms/step - loss: 0.0149 - mse: 0.0149
Epoch 8/30
638/638 [==============================] - 1s 995us/step - loss: 0.0136 - mse: 0.0136
Epoch 9/30
638/638 [==============================] - 1s 1ms/step - loss: 0.0129 - mse: 0.0129
Epoch 10/30
638/638 [==============================] - 1s 996us/step - loss: 0.0125 - mse: 0.0125
Epoch 11/30
638/638 [==============================] - 1s 1ms/step - loss: 0.0122 - mse: 0.0122
Epoch 12/30
638/638 [==============================] - 1s 986us/step - loss: 0.0117 - mse: 0.0117
Epoch 13/30
638/638 [==============================] - 1s 996us/step - loss: 0.0113 - mse: 0.0113
Epoch 14/30
638/638 [==============================] - 1s 986us/step - loss: 0.0114 - mse: 0.0114
Epoch 15/30
638/638 [==============================] - 1s 1ms/step - loss: 0.0108 - mse: 0.0108
Epoch 16/30
638/638 [==============================] - 1s 2ms/step - loss: 0.0106 - mse: 0.0106
Epoch 17/30
638/638 [==============================] - 1s 2ms/step - loss: 0.0104 - mse: 0.0104
Epoch 18/30
638/638 [==============================] - 1s 2ms/step - loss: 0.0098 - mse: 0.0098
Epoch 19/30
638/638 [==============================] - 1s 1ms/step - loss: 0.0097 - mse: 0.0097
Epoch 20/30
638/638 [==============================] - 1s 1ms/step - loss: 0.0096 - mse: 0.0096
Epoch 21/30
638/638 [==============================] - 1s 1ms/step - loss: 0.0097 - mse: 0.0097
Epoch 22/30
638/638 [==============================] - 1s 1ms/step - loss: 0.0096 - mse: 0.0096
Epoch 23/30
638/638 [==============================] - 1s 1ms/step - loss: 0.0096 - mse: 0.0096
Epoch 24/30
638/638 [==============================] - 1s 1ms/step - loss: 0.0094 - mse: 0.0094
Epoch 25/30
638/638 [==============================] - 1s 1ms/step - loss: 0.0093 - mse: 0.0093
Epoch 26/30
638/638 [==============================] - 1s 1ms/step - loss: 0.0091 - mse: 0.0091
Epoch 27/30
638/638 [==============================] - 1s 1ms/step - loss: 0.0093 - mse: 0.0093
Epoch 28/30
638/638 [==============================] - 1s 1ms/step - loss: 0.0093 - mse: 0.0093
Epoch 29/30
638/638 [==============================] - 1s 1ms/step - loss: 0.0085 - mse: 0.0085
Epoch 30/30
638/638 [==============================] - 1s 1ms/step - loss: 0.0088 - mse: 0.0088


Training history across epochs for training data
2022-08-17T14:01:38.763535 image/svg+xml Matplotlib v3.5.1, https://matplotlib.org/ 
54/54 [==============================] - 0s 884us/step
54/54 [==============================] - 0s 884us/step
Vizualization for FDC for training data (shown in dark hue) and predicted clusters from neural network on validation data (shown in corresponding light hues)
2022-08-17T14:01:58.647974 image/svg+xml Matplotlib v3.5.1, https://matplotlib.org/ 
Average percentage of patients belongs to the same cluster is: 94.81152691395197%
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